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Carsten Butz [7]C. Butz [4]Clarence E. Butz [1]Carston Butz [1]
  1. Steve Awodey, Carsten Butz & Alex Simpson (2007). Relating First-Order Set Theories and Elementary Toposes. Bulletin of Symbolic Logic 13 (3):340-358.
    We show how to interpret the language of first-order set theory in an elementary topos endowed with, as extra structure, a directed structural system of inclusions (dssi). As our main result, we obtain a complete axiomatization of the intuitionistic set theory validated by all such interpretations. Since every elementary topos is equivalent to one carrying a dssi, we thus obtain a first-order set theory whose associated categories of sets are exactly the elementary toposes. In addition, we show that the full (...)
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  2. Steve Awodey, Carston Butz, Alex Simpson & Thomas Streicher, Relating First-Order Set Theories, Toposes and Categories of Classes.
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  3. Carsten Butz (2004). Saturated Models of Intuitionistic Theories. Annals of Pure and Applied Logic 129 (1-3):245-275.
    We use the language of categorical logic to construct generic saturated models of intuitionistic theories. Our main technique is the thorough study of the filter construction on categories with finite limits, which is the completion of subobject lattices under filtered meets. When restricted to coherent or Heyting categories, classifying categories of intuitionistic first-order theories, the resulting categories are filtered meet coherent categories, coherent categories with complete subobject lattices such that both finite disjunctions and existential quantification distribute over filtered meets. Such (...)
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  4. S. Awodey & C. Butz (2000). Topological Completeness for Higher-Order Logic. Journal of Symbolic Logic 65 (3):1168-1182.
    Using recent results in topos theory, two systems of higher-order logic are shown to be complete with respect to sheaf models over topological spaces- so -called "topological semantics." The first is classical higher-order logic, with relational quantification of finitely high type; the second system is a predicative fragment thereof with quantification over functions between types, but not over arbitrary relations. The second theorem applies to intuitionistic as well as classical logic.
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  5. C. Butz (2000). Preface. Annals of Pure and Applied Logic 104 (1-3):1-2.
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  6. C. Butz & I. Moerdijk (1999). An Elementary Definability Theorem for First Order Logic. Journal of Symbolic Logic 64 (3):1028-1036.
  7. Carsten Butz (1999). A Topological Completeness Theorem. Archive for Mathematical Logic 38 (2):79-101.
    We prove a topological completeness theorem for infinitary geometric theories with respect to sheaf models. The theorem extends a classical result of Makkai and Reyes, stating that any topos with enough points has an open spatial cover. We show that one can achieve in addition that the cover is connected and locally connected.
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  8. C. Butz, P. Johnstone, J. Gallier, J. D. Hamkins, B. Khoussaiuov, H. Lombardi & C. Raffalli (1998). Andrkka, H., Givant, S., Mikulb, S., Ntmeti, I. And Simon, A. Annals of Pure and Applied Logic 91:271.
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  9. Carsten Butz & Peter Johnstone (1998). Classifying Toposes for First-Order Theories. Annals of Pure and Applied Logic 91 (1):33-58.
    By a classifying topos for a first-order theory , we mean a topos such that, for any topos models of in correspond exactly to open geometric morphisms → . We show that not every first-order theory has a classifying topos in this sense, but we characterize those which do by an appropriate ‘smallness condition’, and we show that every Grothendieck topos arises as the classifying topos of such a theory. We also show that every first-order theory has a conservative extension (...)
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  10. Carsten Butz (1997). Syntax and Semantics of the Logic. Notre Dame Journal of Formal Logic 38 (3):374-384.
    In this paper we study the logic , which is first-order logic extended by quantification over functions (but not over relations). We give the syntax of the logic as well as the semantics in Heyting categories with exponentials. Embedding the generic model of a theory into a Grothendieck topos yields completeness of with respect to models in Grothendieck toposes, which can be sharpened to completeness with respect to Heyting-valued models. The logic is the strongest for which Heyting-valued completeness is known. (...)
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  11. Carsten Butz (1997). Syntax and Semantics of the Logic Llambdaomega Omega. Notre Dame Journal of Formal Logic 38 (3):374-384.
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  12. Carsten Butz (1997). Syntax and Semantics of the Logic $\Mathcal{L}^\Lambda_{\Omega\Omega}$. Notre Dame Journal of Formal Logic 38 (3):374-384.
    In this paper we study the logic $\mathcal{L}^\lambda_{\omega\omega}$, which is first-order logic extended by quantification over functions . We give the syntax of the logic as well as the semantics in Heyting categories with exponentials. Embedding the generic model of a theory into a Grothendieck topos yields completeness of $\mathcal{L}^\lambda_{\omega\omega}$ with respect to models in Grothendieck toposes, which can be sharpened to completeness with respect to Heyting-valued models. The logic $\mathcal{L}^\lambda_{\omega\omega}$ is the strongest for which Heyting-valued completeness is known. Finally, (...)
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  13. Clarence E. Butz & Phillip V. Lewis (1996). Correlation of Gender-Related Values of Independence and Relationship and Leadership Orientation. Journal of Business Ethics 15 (11):1141 - 1149.
    This study compares the relationship between the moral reasoning modes and leadership orientation of males versus females, and managers versus engineers/scientists. A questionnaire developed by Worthley (1987) was used to measure the degree of each participant's respective independence and justice, and relationships and caring moral reasoning modes. Leadership orientation values and attitudes were measured using the Fiedler and Chemers (1984) Least Preferred Coworker Scale.The results suggest that, although males differ from female in their dominant moral reasoning modes, managers are not (...)
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